- Tytuł:
- Topological tensor products of a Fréchet-Schwartz space and a Banach space
- Autorzy:
- Peris, Alfredo
- Powiązania:
- https://bibliotekanauki.pl/articles/1292616.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Fréchet-Schwartz spaces
(DFS)-spaces
topological tensor products
approximation property
compact approximation property - Opis:
- We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that $E ⊗_{ε} X$ is not an inductive limit of normed spaces for some Banach space X. This solves in the negative open questions of Bierstedt, Meise and Hollstein. As a consequence we obtain Fréchet-Schwartz spaces F and Banach spaces X such that the problem of topologies of Grothendieck has a negative answer for $F ⨶_π X$. This solves in the negative a question of Taskinen. We also give examples of Fréchet-Schwartz spaces and (DFS)-spaces without the compact approximation property and with the compact approximation property but without the approximation property.
- Źródło:
-
Studia Mathematica; 1993, 106, 2; 189-196
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł